Problem: What do the following two equations represent? $-3x+3y = -2$ $-9x+9y = -2$
Answer: Putting the first equation in $y = mx + b$ form gives: $-3x+3y = -2$ $3y = 3x-2$ $y = 1x - \dfrac{2}{3}$ Putting the second equation in $y = mx + b$ form gives: $-9x+9y = -2$ $9y = 9x-2$ $y = 1x - \dfrac{2}{9}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.